On the Essence of Discovery

When progress in science entails revolutionary shifts in world view, controversy inevitably follows. The Big Bang theory—that the universe, rather than being static, underwent an explosive expansion starting from a special point in time roughly fourteen billion years ago, and continues to expand—is universally accepted today, but was rejected and even ridiculed by many senior experts early on. Such intense reactions presumably stem from the unpleasant disorientation inherent in having one’s fixed and seemingly well-validated ideas challenged and potentially overturned.1 While less earth-shattering than the Big Bang theory, the discovery twenty years ago that the expansion of the universe is actually accelerating again upended many assumptions about cosmology and fundamental physics. It is this observational discovery, along with certain technical advances in understanding the mathematics of string and quantum field theories, that lies at the root of the interest in the set of ideas known as the multiverse.

Ellis’s essay reads as just such a curmudgeonly reaction. While much of what he writes about modern theories of the multiverse is correct, some is badly misleading or polemical. After mentioning several pieces of observational evidence that could support or falsify a class of multiverses, Ellis comments that the putative evidence “might be the result of a statistical fluctuation… The inference to the multiverse is not obligatory.” This is true, but also misses the mark entirely. The same could be said of any piece of experimental evidence for any scientific theory. While cosmology does suffer from the significant difficulty that it cannot repeat experiments as one can in laboratory science, that has not prevented cosmologists from reaching very surprising, yet firm and statistically well-supported, conclusions about our universe, such as the aforementioned Big Bang and accelerating expansion of the universe.

Ellis provides a long list of different conceptions of the multiverse, apparently in an attempt to convince the reader that the idea is ill-defined and unscientific. In this he is somewhat successful; it is certainly the case that the term multiverse has been used to refer to a host of disparate and sometimes mutually contradictory or even nonsensical ideas. The same could be said of the term evolution, to pick one example from many. This semantic point does not indicate that any one of the specific ideas and theories that fall under this general rubric are necessarily ill-defined or unscientific. To make matters worse, Ellis fumbles a number of technical points, for instance where he questions the mathematical viability of one kind of eternal inflation by referring to a paper about a different kind.

The heart of Ellis’s criticism is that certain modern theories in physics—he singles out string theory and theories of the multiverse—have become disconnected from experiment. He presents this as deeply problematic, and asserts that it is some sort of major departure from historical practice: “Scientific theories have since the seventeenth century been held tight by an experimental leash.” Leaving aside the fact that he later refers to specific experimental tests of the multiverse, I find this criticism naive. Cosmology was almost entirely unmoored from experiment until the twentieth century, when advances in telescope technology made the relevant observations possible. More importantly, what precisely is the definition of theories of physics, and why must all of them live or die by experiment? Since long before the seventeenth century and even more so today, mathematicians have unabashedly pursued abstract ideas with no connection to experiment whatsoever. Theoretical physics as a discipline can be regarded as adjacent to mathematics, separated from it by a rather fuzzy and permeable boundary. There is a long-standing tradition of mathematical physics, research that pursues the implications of mathematical ideas and models, with at best half an eye towards experiment and physical phenomena. An example is the study of percolation, a mathematical model originally conceived to describe liquid permeating a substance—but highly idealized and in two dimensions, where the mathematics is simple enough to be tractable but rich enough to be interesting. It turns out that the mathematical tools and insights developed studying a toy model have found application in many areas ranging from epidemiology to cellular telephone networks to string theory, yet are totally useless for designing a better filter coffee maker. Indeed, such basic research rarely goes to waste, but it is extremely difficult to predict where it will eventually find its most impressive application.

Contrary to Ellis’s assertions, the history of physics is full of people working on mathematical ideas that are not testable experimentally. While some such ideas failed to make a lasting impact, others led to major advances in both practical technology and our fundamental understanding of the world. The essence of discovery is that you do not know what you will find until you look. Attempts to stifle this pursuit of knowledge are counterproductive, divisive, and ultimately futile.

Matthew Kleban

George Ellisreplies:

The key point in Matthew Kleban’s response is to say:

the putative evidence “might be the result of a statistical fluctuation… The inference to the multiverse is not obligatory.” This is true—but misses the mark entirely, as the same could be said of any piece of experimental evidence for any scientific theory.

Wrong, cosmology is not just any old scientific theory; it is a very special theory, because of the uniqueness of the universe. Cosmology is not about existence of families of particles or types of forces; it is a historical and geographical science referring to existence of specific configurations of matter—the Virgo Cluster, the Great Attractor, and so on—and their specific history—a hot big bang era for a particular length of time, a subsequent matter-dominated era for a specific length of time, and so on. Thus the issue of whether what we see is a statistical fluctuation or not is a key issue quite unlike what happens in particle physics. It is the question of Cosmic Variance.2 Do variations from our theoretical predictions— the excess CMB angular power at large angles is an example—imply we need a theory revision? Or are they there because the single universe that actually exists differs from the statistical predictions of our theories by so little that this discrepancy can just be accepted as a fluke? We cannot observe other universes to decide. All we can do is observationally confirm or disprove that the one universe domain we do have access to differs from our theories by a certain amount and make our decision. We then have to make a decision as to how to interpret this outcome, which is, in the end, a philosophical decision, as one cannot test experimentally or observationally whether this decision is correct or not. This is quite unlike analyzing the statistics of collision events at the LHC when each collision provides new data on the repeatable behavior of all matter. The experimental sciences and historical/geographic sciences are crucially different, and even more so in the case of cosmology, because of the uniqueness of the universe. There is no other entity that it can be compared to.

He ends:

The history of physics is full of people working on mathematical ideas that are not testable experimentally. While some such ideas failed to make a lasting impact, others led to major advances in both practical technology and our fundamental understanding of the world. The essence of discovery is that you do not know what you will find until you look. Attempts to stifle this pursuit of knowledge are counterproductive, divisive, and ultimately futile.

I agree, and I do not advocate stifling any such research. I advocate that this pursuit continues to aim to develop experimental and observational tests of the relevant theories, but that it be very cautious in making any claims in those cases where it turns out there are no such tests.

“The essence of discovery is that you do not know what you will find until you look.” Indeed. But if you cannot look, which is the case we are talking about, this philosophy runs into a dead end. There is, of course, a subset of multiverse models, involving bubble collisions, that are testable in principle,3 and some have claimed that they have indeed been seen through a cold spot in the CMB sky.4 The majority of cosmologists do not agree. It is the pesky issue of cosmic variance just mentioned; that cold spot is assumed by most to be just a statistical fluctuation. In any case, all the multiverse proposals that do not involve bubble collisions are not testable in this way. The idea of doing such tests to see if there is evidence of such collisions is not part of mainstream cosmology—see, for example, the Planck team’s data analysis.5 And some take the prediction of multiverses by many inflationary theories as prime facie evidence that those theories are incorrect.6

Matthew Kleban is Associate Professor of Physics and Director of the Center for Cosmology and Particle Physics at New York University.

George Ellis is Emeritus Distinguished Professor of Complex Systems in the Department of Mathematics and Applied Mathematics at the University of Cape Town in South Africa.

Of course, leading scientists also reject and ridicule ideas that turn out to be wrong, so one should be careful not to regard such a reaction in itself as evidence that an idea is correct! &larrhk;